Abstract: The functional integral for gravity poses numerous challenges, one of which is simply deciding the nature of the set of spacetime histories over which one should sum. I will propose an answer to this question in terms of a natural discretization of gravity, which is based on causal structure and the imposition of a finite number of degrees of freedom in a compact region of spacetime. Given a recently discovered form for an action functional on such histories, I will present a numerical exploration of some features of the resulting functional integral, including a characterization of the phase space of the analytically continued sum. The results point to evidence that the dynamically preferred spacetime histories have a two dimensional character as one approaches the Planck scale.